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arXiv · 1912.05574

Liouville type theorems on manifolds with nonnegative curvature and strictly convex boundary

Qianqiao Guo·Fengbo Hang·Xiaodong Wang
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Abstract

We prove some Liouville type theorems on smooth compact Riemannian manifolds with nonnegative sectional curvature and strictly convex boundary. This gives a nonlinear generalization in low dimension of the recent sharp lower bound of the first Steklov eigenvalue by Xia-Xiong and verifies partially a conjecture by the third author. As a consequence, we derive several sharp Sobolev trace inequalities on these manifolds.

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Qianqiao Guo, Fengbo Hang, Xiaodong Wang. 2019-12-11. Liouville type theorems on manifolds with nonnegative curvature and strictly convex boundary. https://arxiv.org/abs/1912.05574

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